Abstract
An analytical approach is developed to calculate crystal-field parameters in rare-earth intermetallics. Unlike the point-charge approach, the model includes all electrostatic crystal-field contributions and accounts for charge penetration of 4f and non-4f electrons. The conduction electrons of the intermetallic alloy are considered as a weakly disturbed homogeneous electron gas with inverse Thomas-Fermi screening length q. Asymptotically, the screened-charge model yields A 0 2ocr −m exp(- qr) with m = 1, as opposed to the screened point-charge model, where m = 3. The properties of the atoms which create the crystal-field enter the theory as crystal-field charges Q cf. Methods to calculate Q cf are presented, and it is shown that Q cf contains a negative contribution due to the finite size of the electronic cores of the surrounding atoms. For instance, helium atoms, which are strongly neutral, are predicted to bear a crystal-field charge Q cf= - 0.64 e in a q = 3 Å−1 electron gas. It is shown how the properties of the rare-earth ion affect the crystal-field parameters and an analytical expression for the dependence of A 0 2 on the ratio (r4) 4f/ (r2)4f is obtained. Interstitially modified iron-rich rare-earth intermetallics are used to discuss the A 0 2 dependence on distance and chemical nature of the surrounding atoms.